COMPUTING APPROXIMATE SOLUTIONS OF THE MAXIMUM COVERING PROBLEM WITH GRASP

We consider the maximum covering problem, a combinatorial optimization problem that arises in many facility location problems. In this probl em, a potential facility site covers a set of demand points. With each demand point, we associate a nonnegative weight. The task is to selec t a subset of p > 0 sites from the set of potential facility sites, su ch that the sum of weights of the covered demand points is maximized. We describe a greedy randomized adaptive search procedure (GRASP) for the maximum covering problem that finds good, though not necessarily o ptimum, placement configurations. We describe a well-known upper bound on the maximum coverage which can be computed by solving a linear pro gram and show that on large instances, the GRASP can produce facility placements that are nearly optimal.